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Vicious circles: on the mathematics of non-wellfounded phenomena
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Universal coalgebra: a theory of systems
Theoretical Computer Science - Modern algebra and its applications
Coinductive Proof Principles for Stochastic Processes
LICS '06 Proceedings of the 21st Annual IEEE Symposium on Logic in Computer Science
On fixed points of strictly causal functions
FORMATS'13 Proceedings of the 11th international conference on Formal Modeling and Analysis of Timed Systems
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Metric coinduction is a form of coinduction that can be used to establish properties of objects constructed as a limit of finite approximations. One can prove a coinduction step showing that some property is preserved by one step of the approximation process, then automatically infer by the coinduction principle that the property holds of the limit object. This can often be used to avoid complicated analytic arguments involving limits and convergence, replacing them with simpler algebraic arguments. This paper examines the application of this principle in a variety of areas, including infinite streams, Markov chains, Markov decision processes, and non-well-founded sets. These results point to the usefulness of coinduction as a general proof technique.